Complex Oxygen Regimes of Water Objects Under the Anthropogenic Loading

Abstract

Under conditions of intense anthropogenic loading in combination with climate change, the significant degradation of water resources of the planet, especially surface waters, is observed. The surface waters are the environment where a vast part of natural ecosystems dwell, and provide the major source of drinking water. They are also an extremely important element of technological processes in industry, agriculture, and etc. Therefore, the assessment, control, and forecasting of surface water quality are in a focus of many scientific investigations. This report deals with the oxygen regime of water objects (basins of self-purification) which is studied by the methods of mathematical modeling. The oxygen regime description consists of the balance equations governing the dynamics of oxygen, i.e. biochemical oxygen demand (BOD) and dissolved oxygen (DO), phosphorus, and phytoplankton. The resulting nonlinear dynamical system is studied by the numerical and qualitative analysis methods. It is shown that the model possesses the steady solutions in a vicinity of which the nonlinear periodic regimes can occur. When the parameters of nonlinearity vary, the periodic regimes lose their stability and multiperiodic regimes appear. Among complex system’s solutions, there are also chaotic regimes. Furthermore, we developed the model for the river system which consists of coupled dynamical systems describing the bio-chemical processes in two connecting self-purificating basins. This model possesses the nonlinear periodic regimes as well.